In general, it is impossible to completely remove errors in decoding. If an error, which occurs once, infinitely affects data to be decoded thereafter (decoder such as this is said to be catastrophic), efficient data tranfer will become impossible. This is because the number of data bits to be transferred must be sufficiently reduced so that errors do not occur. In practice, when a convolutional code is used as a recording code, there are some cases where the convolutional code will have an infinite influence on decoded data. Therefore, in such a case, special consideration has to be given to a sequence of generated signals.
The reason why the aforementioned inconvenience occurs is because there is memory in a channel, so this inconvenience occurs not only in a digital channel but in an analog channel. Particularly, in a case where a signal from a magnetic storage medium is processed, the inter-symbol interference corresponds to the memory of the channel and there is the possibility that errors will infinitely propagate.
Even if there were a possibility such as this, the use of PRML using inter-symbol interference positively would become very important for realizing higher recording density and faster transmission speed in a magnetic storage unit such as a hard-disk drive unit.
In PRML, the value of a likelihood function calculated in some form is compared with a certain reference value in order to decode original data. In a case where there are a plurality of reference values, it is to be checked whether the value of the likelihood function is within a certain decision area. If inter-symbol interference does not occur in a received signal, the aforementioned reference value will always be constant. However, in a case where inter-symbol interference exists, the reference value must be changed in correspondence with data pattern decoded before a signal to be decoded, or the influence of the inter-symbol interference must be removed from a received signal to calculate a likelihood function. Now consider the former case. In a case where a mistaken reference value is selected for some influence, a previously decoded data pattern is varied by the error, and consequently, there is the possibility that error propagation will infinitely continue.
As a conventional method for suppressing error propagation, there are the following methods used in magnetic recording.
(1) Propagation suppressing method where bit missing or bit insertion is detected by always checking the polarity of a received signal when decoding the signal. This method is described in Arvind M. Patel, "A New Digital Signal Processing Channel for Data Storage Product," IEEE Transaction on magnetic Vol. 27, No. 6, November 1991.
The method cannot cope with a case where peak shift, which is not bit missing or bit insertion, occurs. By way of example, there is a case where +1, 0, -1, 0, +1, and 0 are shifted to 0, +1, 0, -1, 0, and +1.
(2) Method where a decoder is reset or synchronization is recovered by burying specific patterns in data bits and thereby cutting off inter-symbol interference. If a method such as this is used, this method cannot be realized at all times while holding the capacity of the channel of a code to more than a certain level. Specifically, in the (1, 7) RLL (run-length-limited) recording codes, the logical limit of the channel capacity is 0.6793 (see Kees A. Schouhamer, "Coding Technique for Digital Recorders," Immink) and therefore the code rate constitutes 2/3 of data bits. However, if specific patterns are buried, then the logical limit will be considerably reduced and the code whose rate is 2/3 has not been constituted.
(3) Method which allows error propagation to occur at specific patterns and where data are randomized so as to prevent such pattern form continuously occurring. In practice, this method is widely used, but it is a probabilistic method and the propagation length is comparatively long.